A triangular garden plot has one 16 foot side. The height perpindicular to that side is 12 feet 6 inches. If each plant requires 36 sq. in. of space, how many plants can be placed in the plot?
Divide the area of the triangle by the area required per plant. That will give you the number of plants.
Make sure both are in the same units (square feet or square inches).
36 in^2 = 0.25 ft^2
triangle area = (1/2) base x height
To find the area of the triangular garden plot, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, we have the base as 16 feet and the height perpendicular to that side as 12 feet 6 inches. However, we need to convert the height to feet because the base is already in feet.
To convert 12 feet 6 inches to feet, we divide the inches by 12 (since there are 12 inches in a foot).
12 feet 6 inches = 12 + (6 / 12) = 12.5 feet
Now we can substitute the values into the formula:
Area = (1/2) * 16 feet * 12.5 feet
= 8 feet * 12.5 feet
= 100 square feet
Next, we need to convert the required space per plant, which is 36 square inches, to square feet.
To convert 36 square inches to square feet, we divide by 144 (since there are 144 square inches in a square foot).
36 square inches = 36 / 144 = 0.25 square feet
Now that both the area of the plot and the required space per plant are in square feet, we can divide the area of the plot by the area required per plant:
Number of plants = Area of plot / Area required per plant
= 100 square feet / 0.25 square feet
= 400 plants
Therefore, you can place 400 plants in the triangular garden plot.